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Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

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BuyFindarrow_forward

Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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Let S be the set of all strings of a ' s  and b ' s .

  1. Define f : S Z as follows: For each string s in S
  2.    f ( s ) = { the number of b ' s to the left of the left-most a in s 0 if s contains no a ' s .

Find f ( a b a ) , f ( b b a b ) , and  f ( b ) . What is the range of f?

  • Define g : S S as follows: For each string s in S.
  • g ( s ) =  the string obtained by writing the characters of s in reverse order.
    Find g ( a b a ) , g ( b b a b ) , and g ( b ) . What is the range of g?

    To determine

    (a)

    Find f(aba),f(bbab) and f(b). What is the range of f ?

    Explanation

    Given information:

    Find f(aba),f(bbab) and f(b). What is the range of f ?

    Concept used:

    The range of such a function f is {0}Z+.

    Calculation:

    f(aba)=0

    The leftmost variable in the string is an a, and so it has no b variables on its left.

    f(bbab)=2

    There is only one a, and so it is the leftmost a

    To determine

    (b)

    Find g(aba),g(bbab),andg(b). What is the range of g ?

    To determine

    (c)

    Find

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